Sharpen Your Eye for Trot Diagonals

I ran across a Facebook discussion about how to tell and how to teach when a rider is on the correct diagonal at the trot, so I thought

Why Do You Teach Trot Diagonals in Horseback Riding Lessons?

Have you ever considered the reason behind why you teach trot diagonals? Do you teach it because it was taught to you? Do you teach it as a